Warwick Centre for Complexity Science
MathSys CDT MSc Project outline
Fragment (Missile) Modelling
Supervisors: Jan Stene (DNV GL) and Samuel Johnson (Complexity and Mathematics)
Consequence modelling and risk assessment associated with potential accidents in the
petro-chemical industry is a field of active research as the industry strives to better understand their
risks and improve on their mitigation strategies.
Accidental hazardous events may be split into two categories: primary and secondary events. The
distinction is that primary events happen first and may then cause secondary events to occur. The
consequences of a secondary event could potentially be more serious than direct consequences of
the related primary event, and therefore such potential ‘domino’ effects are very important to
consider when carrying out a risk assessment.
For processes involving flammable materials, radiation from a fire and overpressure from an
explosion are typical examples of primary accidents that could cause domino effects by destroying
nearby process equipment containing additional amounts of flammable material. Another potential
cause of domino effects is the projection of fragments, for example following a BLEVE (boiling
liquid expanding vapour explosion). Such projected fragments may destroy nearby processing
equipment or injure/kill people by direct impact.
DNV GL’s software products Phast and Safeti for consequence and risk modelling do currently not
account for projected fragments, and it is therefore of interest to us to bridge this gap. For the
purposes of an MSc project, fragment modelling may include (but not necessarily limited to) the
following:
• Literature review on fragment modelling (sometimes referred to as missile modelling)
• Theory and model development:
o Equations of motion of projected fragment with analytical solutions if applicable
 One example of the description of motion is by a system of second-order
differential equations
o Initial velocity and angle of project may be modelled as stochastic variables
o Could apply a Monte Carlo method to estimate the probability that a fragment
originated from a vessel could hit a specific target placed at a distance r. Within the
Monte Carlo procedure, quantities like the departure angle and the initial velocity
may be assumed to vary randomly
o One key result could be the impact probability as a function of spatial position of
target
• Numerical solution algorithm as appropriate
• Implementation (e.g. Matlab) to produce and discuss results